Circumcenter Formula

Circumcenter refers to the circumcenter of a triangle. The point where the perpendicular bisectors of a triangle meets. It lies inside for an acute, outside for an obtuse and at the center of the hypotenuse for the right triangle.

Method to Calculate the Circumcenter of aTriangle

The steps to find the circumcenter of a triangle:

Find and Calculate the midpoint of given coordinates or midpoints (AB, AC, BC)

Calculate the slope of the particular line

By using the midpoint and the slope, find out the equation of line (y-y1) = m (x-x1)

Find out the other line of equation in the similar manner

Solve the two bisector equation by finding out the intersection point

Calculated intersection point will be the circumcenter of the given triangle

Solved Examples

Question 1: If three coordinates of a triangle are (3,2), (1,4), (5,4). Calculate the circumcenter of this triangle ?

Solution:

Given points are,
A = (3, 2), B = (1, 4), C = (5, 4)
To find out the circumcenter we have to solve any two bisector equations and find out the intersection points.